SYZ mirror conjecture predicts that a Calabi–Yau manifold X consists of a family of tori which are dual to a family of special Lagrangian tori on the mirror dual manifold . Here we consider a fibration of polarized abelian varieties and we construct a dual one. Moreover we prove that they are equivalent at the level of derived categories.
La conjecture de « symétrie miroir SYZ » prédit quʼune variété de Calabi–Yau X consiste en une famille de tores qui sont duaux dʼune famille de tores lagrangiennes spéciaux dans la variété miroir duale . Nous considérons ici une fibration de variétés abéliennes polarisées et nous en construisons la duale. De plus, nous montrons quʼelles sont équivalentes au niveau des catégories dérivées.
Accepted:
Published online:
Cristina Martínez 1, 2
@article{CRMATH_2012__350_13-14_689_0, author = {Cristina Mart{\'\i}nez}, title = {Abelian fibrations and {SYZ} mirror conjecture}, journal = {Comptes Rendus. Math\'ematique}, pages = {689--692}, publisher = {Elsevier}, volume = {350}, number = {13-14}, year = {2012}, doi = {10.1016/j.crma.2012.07.011}, language = {en}, }
Cristina Martínez. Abelian fibrations and SYZ mirror conjecture. Comptes Rendus. Mathématique, Volume 350 (2012) no. 13-14, pp. 689-692. doi : 10.1016/j.crma.2012.07.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.07.011/
[1] Les intersections complètes de nieveau de Hodge un, Invent. Math., Volume 15 (1972), pp. 237-250
[2] Mirror symmetry and elliptic curves, Texel Island, 1994 (Progr. Math.), Volume vol. 129, Birkhäuser, Boston, MA (1995), pp. 149-163
[3] Torus fibrations, gerbes, and duality (in Memoirs of the AMS) | arXiv
[4] Relative integral functors for singular fibrations and singular partners, J. Eur. Math. Soc. (JEMS), Volume 11 (2009), pp. 597-625
[5] Derived equivalences of Calabi–Yau fibrations | arXiv
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